Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
478 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20284750 | C2 | semidirect |
| 5. #20273058 | C2 | semidirect |
| 6. #20272576 | C2 | semidirect |
| 7. C53×#1537 | C2 | semidirect |
| 187. #1537 | D53 | semidirect |
| 221. C53 | #10041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285722 | 2 |
| #20284838 | 2 |
| #20284750 | 2 |
| #20273183 | 2 |
| #20273058 | 2 |
| #20272576 | 2 |
| C53×#1537 | 2 |
| #10041 | 53 |